Chapter 6: Q3P (page 314)

$x y d x + x^{2} d y$ where C is as selected.

Short Answer

Expert verified

The integral will give the solution to be $\frac{14}{3}$ .

Step by step solution

Given information

The given equation is $x y d x + x^{2} d y,$ .

Definition of conservative force and scalar potential

A force is said to be conservative if $\nabla \times F = 0 .$ .

The scalar potential is independent of the path. The scalar potential is the sum of potential in all the 3 dimensions calculated separately.

The formula for the scalar potential is $W = \int F . d r$ .

Use Greens Theorem

Takethe values as mentioned below.

$P = x y Q = x^{2}$

Use the Green theorem.

$\oint x y d x + x^{2} d y, \iint x d y d x \int_{1}^{4} \int_{0}^{\sqrt{x}} x d y d x \int_{1}^{4} \sqrt{x d x} \frac{16}{3} - \frac{2}{3} \frac{14}{3}$

Hence the integral will give the solution to be $\frac{14}{3}$ .

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$x y d x + x^{2} d y$ where C is as selected.

Short Answer

Step by step solution

Given information

Definition of conservative force and scalar potential

Use Greens Theorem

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xydx+x2dywhere C is as selected.

Short Answer

Step by step solution

Given information

Definition of conservative force and scalar potential

Use Greens Theorem

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Fluids

Radiation

Rotational Dynamics

Circular Motion and Gravitation

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Study anywhere. Anytime. Across all devices.

$x y d x + x^{2} d y$ where C is as selected.